三值量子逻辑进路探析

量子测量实验显示部分经典逻辑规则在量子世界中失效。标准量子逻辑进路通过特有的希尔伯特空间的格运算揭示出一种内在于微观物理学理论的概念框架结构,也即量子力学测量命题的正交补模或弱模格,解释了经典分配律的失效,它在形式化方面十分完美,但在解释方面产生了一些概念混乱。在标准量子逻辑进路之外,赖欣巴赫通过引入"不确定"的第三真值独立地提出一种不同的量子逻辑模型来解释量子实在的特征,不是分配律而是排中律失效,但是他的三值量子逻辑由于缺乏标准量子逻辑的上述优点而被认为与量子力学的概率空间所要求的潜在逻辑有很少联系。本文尝试引入一种新的三值逻辑模型来说明量子实在,它有以下优点:(1)满足卢卡西维茨创立三值逻辑的最初语义学假定;(2)克服赖欣巴赫三值量子逻辑的缺陷;(3)澄清标准量子逻辑遭遇的概念混乱;(4)充分地保留经典逻辑规则,特别是标准量子逻辑主张放弃的分配律。     

推理与偏差:从传统逻辑到逻辑直觉的推进

近来研究发现双加工理论中基于分析性思维的逻辑或概率加工也可以进行快速的直觉加工,引发了一种叫做“逻辑直觉”的提议。不同范式(冲突检测、双指导语、喜好范式、随机反应)下的实证研究对逻辑直觉存在的稳定性提供了支持。逻辑直觉具有自动性和内隐性两个核心特点。虽然逻辑直觉对于偏差解释、理论革新和人类理性的讨论都有重要影响,但逻辑直觉的研究目前还处于起步阶段,仍有许多不足之处需要更多的研究者去探索。     

关于诊断的逻辑方法与误诊的逻辑思考

关于诊断的逻辑方法与误诊的逻辑思考河南医科大学第一附属医院（郑州４５００５２）熊卫东河南医科大学自然辩证法教研室赵兴太一、临床诊断中的逻辑程序１．搜集资料：临床资料的搜集是对病情的调查研究,包括采取病史、体格检查和作辅助检查三方面的内容。临床诊断的各...     

从逻辑哲学看模糊逻辑的形式化

从逻辑哲学观点看,在“符号化、公理化的模糊逻辑”与非形式化的“人脑使用的模糊逻辑”（苗东升的说法）这两者之间,只是形式模型及其现实原型的关系,决不相互排斥。真正的问题不在于,在现实生活中人脑所使用的实际上行之有效的模糊推理,是否应该和可能符号化、公理化,而是在于如何恰当地进行形式化。笔者采用苏珊·哈克（Susan Haack）的逻辑哲学观点,认为非经典逻辑可划分为扩展逻辑和异常（deviation）逻辑,模糊逻辑归属于异常逻辑。本文以模糊逻辑系统FZ为例,具体分析了虽然经典逻辑中一些较强的公理和推理规则均不成立,但是与之对应的较弱的“合经典的”（well-behaved）公理和推理规则却仍然可以成立,由此导致一系列新奇性质。笔者采用了达·柯斯塔（da Costa）的形式化技巧,它是关于“在虚设不矛盾律成立的前提下”（相应公式可以称为“合经典的”）才能成立的逆否律。当我们撤除了“虚设不矛盾律为前提”的限定,它又重新回到了无条件成立的情况。笔者也推广了玻尔（N.Bohr）和冯·威扎克（von Weizsaecker）关于对应原理的思想,认为作为非经典逻辑的模糊逻辑与经典逻辑之间也应当遵守“对应原理”：经典逻辑是模糊逻辑的前身,模糊逻辑将构成更为普遍的逻辑形式,经典逻辑作为模糊逻辑的极限形式,在局部情况下还保持自身的意义。     

论逻辑后承概念

塔尔斯基在其1933年的论文中基于自己开创的语义学定义了形式化语言中真这个概念。然后,他在发表于1936年的本文中,在真这个概念的定义的基础上,第一次为后承概念提出了一个实质恰当的定义,即“句子X从类K的句子逻辑地得出当且仅当K这个类的每个模型也是句子X的模型”,使得逻辑后承这个现代逻辑核心概念的定义成为标准定义。但是,这个定义也遗留了一个更为根本的问题,即逻辑词项和非逻辑词项的划分标准问题,后者将由塔尔斯基本人在1966年给出了一个划分标准,从而开辟了一个方兴未衰的逻辑哲学研究方向。     

儒家智者的逻辑——析荀子正名论

荀子适应当时社会需要 ,从儒家智者的视角 ,创发孔子正名的逻辑内涵 ,建构以概念论为中心的逻辑体系 ,继墨辩之后把中国古代逻辑推向又一高峰。荀子对概念论和语言论、本体论、认识论、判断论、推理论、诡辩论、语言规范化、华夏大一统的相关论述 ,是当前仍有积极价值的学术精华。以现代方法揭示荀子正名论的逻辑意义 ,是中国逻辑元研究的课题。     

模糊性知识的语境逻辑分析

模糊性问题是当下机器智能化面临的主要难题之一,因此"如何消除知识的模糊性问题"成为当下机器智能化研究的主要方向。本文从两种不同语境逻辑的视角出发,分别诠释了谓词模糊问题与主词或句子的语义模糊问题的回避方式,为模糊问题的解释与表征提供了新方法。事实上,模糊问题是由于语境的不确定性所致,因此语境逻辑的分析方法将是模糊问题解决的主要方式。     

四卡问题解决中的内容与逻辑分析效应

选取条件概率(P(Q|P))由低到高的四个命题作为四卡问题中的检验规则,探讨了大学生被试对四张卡片的逻辑证明作用的推断能力及其对解决四卡问题的影响。结果发现:(1)不同条件概率的命题之间正确选择P-Q的人数百分比不存在显著差异,命题的条件概率因素对四卡问题的正确解决没有影响。(2)逻辑分析过程对四卡问题的正确解决产生了一定的抑制作用,这可能是因为被试不能从整体上思考四张卡片在命题检验中的逻辑作用的缘故。(3)一些被试即使在逻辑分析过程中表现出知道-Q卡片的证伪作用,仍然倾向于选择卡片Q而非-Q,这一现象再次证实了人类思维的非形式逻辑的一面。     

亚里士多德和墨家的逻辑和语言概念

亚里士多德逻辑和墨家逻辑是基于非常不同的本体论思想的。这可以从比较亚里士多德的＂类＂（genus）概念和墨家的＂类＂概念得到解释。传统的翻译把中文词＂同＂和＂异＂分别解释为＂相似＂和＂不同＂,以掩饰这两个概念的不同。据此,亚里士多德逻辑的理论意图是完全不同于具有实际意图的、作为论证指导的墨家逻辑。     

公共管理学科建设:逻辑、核心与基础

从普遍性角度看,任何一个学科建设都应遵循基本的"学术逻辑",这一逻辑主要表现为:从阅读到发表的独立研究,以及这一独立研究需要拓展到两个场域,一是在教室中展开的教学活动,二是参加学术会议与进行学术对话。另外,任何一个学科建设的核心乃是形成"师生学术共同体",而终极目标就是构建"学术流派"。从特殊性的角度看,公共管理学科建设必须在学术思想史、概念体系与研究方法的多样性等方面加以强化。     

Absolute Probability Functions for Intuitionistic Propositional Logic

Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus complete in the probabilistic sense. As there are theorems of classical (propositional) logic that are not intuitionistic ones, there are unary probability functions for intuitionistic logic that are not classical ones. Provided here because of this is a means of singling out the classical probability functions from among the intuitionistic ones.     

A Logic For Inductive Probabilistic Reasoning

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone.     

概率性输入,噪音“与”门(PINA)模型

当前认知诊断测验的主要目的是对被试进行合理分类,进而采用类别变量去描述被试对某技能或知识(即认知属性)的掌握情况,但该粗糙的分类方法不能精细地区分不同被试之间的差异。对此,采用掌握概率这一连续变量去描述被试对某认知属性的掌握情况是一种值得尝试的做法。本文首先基于高阶潜在特质(简称"潜质")模型给出了认知属性掌握概率的量化定义,之后与多成分潜质模型相结合提出了概率性输入,噪音"与"门(PINA)模型;其次,采用MCMC算法实现了对PINA的参数估计,结果表明参数估计程序对各参数的估计返真性均较好;最后,以ECPE数据为例来说明PINA在实际测验分析中具有可行性。     

非参数认知诊断方法下诊断结果的概率化表征

非参数认知诊断分类方法非常适合课堂评估,其诊断结果采用0-1形式而缺乏概率化表征,不能精细地区分被试属性掌握程度的差异或变化,还缺乏可用于评价真实测验分类结果的信度和效度指标。要刻画被试属性掌握程度的差异,首要的问题是要为非参数认知诊断方法提供一种可以量化属性掌握概率的方法。针对此问题,基于二项分布和玻尔兹曼分布提出非参数认知诊断方法下诊断结果的概率化表征方法,并用于构建分类准确性和分类一致性指标。模拟研究与实测数据分析结果显示：概率化表征方法与非参数认知诊断方法的分类结果高度一致;概率化表征方法与认知诊断模型所得的属性掌握概率十分接近;概率化表征方法所得的属性（模式）掌握概率可用于计算属性（模式）分类准确性和分类一致性指标,在实际测验情景下可作为信度和效度指标,评价诊断结果的重测一致率和判准率。     

Hybrid Probabilistic Logic Programs as Residuated Logic Programs

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics.     

Ambiguous comparative judgment: Fuzzy set model and data analysis

Abstract:  This paper proposed two types of fuzzy set models for ambiguous comparative judgments, which did not always hold transitivity and comparability properties. The first type of model was a fuzzy theoretical extension of the additive difference model for preference that was used to explain ambiguous preference strength. The second was a fuzzy logic model for explaining ambiguous preference in which preference strength was bounded, such as a probability measure. In both models, multi-attribute weighting parameters and all attribute values were assumed to be asymmetric fuzzy L-R numbers. For each model, a method of parameter estimation using fuzzy regression analysis was proposed. Numerical examples were also provided for comparison. Finally, the theoretical and practical implications of the proposed models were discussed.     

面向“为学习而测评”的纵向认知诊断模型

基于“为学习而测评”的理念,以促进学生学习为目的,客观量化学习现状并提供诊断反馈的测评模式日益受到重视。相比于横断认识诊断测评,纵向认知诊断测评更有利于实现促进学生发展的目标。为使国内学者系统性地了解纵向认知诊断模型,首先,依据建模逻辑将已有纵向认知诊断模型划分为基于潜在转换分析的和基于高阶潜在结构模型的两类,并逐一介绍和说明两类模型的理论基础和应用情景;然后,通过模拟研究为读者呈现如何使用纵向认知诊断模型进行数据分析及如何解读相应的诊断结果。最后,提炼出四个可进一步研究的议题。     

Quantifying definitional relations in psychological measurement

Quantitative inferences about psychological attributes, such as extraversion, depression and empathy, involve measurement instruments as well as mathematical models that specify how indicators should be aggregated. The type of model that is appropriate for doing so is conditional on the type of relation that exists between an attribute, its facets and its indicators. The common assumption is that such relations are causal relations. Here, instead, we address definitional attribute-facet relations. Our aim is to find an appropriate mathematical model for when an attribute is defined in terms of facets, instead of causing or being caused by facets. In doing so, we describe the semantics of definitions in logical form. From this form we then derive continuous functions for attribute-facet relations using fuzzy logic. A model with main effects and interactions between facets seems to be more powerful for representing definitional relations than traditional formative and reflective models. This has important implications for measurement in basic and applied research.     

Probabilities on Sentences in an Expressive Logic

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter)examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.     

A Propositional Dynamic Logic with Qualitative Probabilities

This paper presents an -completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.